SOLUTION: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 11 cm/min. At what rate must air be removed when the radius is 9 cm?

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Question 1060486: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 11 cm/min. At what rate must air be removed when the radius is 9 cm?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A spherical balloon is to be deflated so that its
radius decreases at a constant rate of 11 cm/min.
At what rate must air be removed when the radius
is 9 cm.

V%22%22=%22%22expr%284%2F3%29%2Api%2Ar%5E3

dV%2Fdt%22%22=%22%224%2Api%2Ar%5E2%2Aexpr%28dr%2Fdt%29

dV%2Fdt%22%22=%22%224%2Api%2A%28matrix%281%2C2%2C9%2Ccm%29%29%5E2%2A%28matrix%281%2C2%2C-11%2Ccm%2Fmin%29%29

matrix%281%2C4%2CdV%2Fdt%2C%22%28at%22%2Cthat%2C%22instant%29%22%29%22%22=%22%22matrix%281%2C2%2C-396pi%2Ccm%5E3%2Fmin%29

The negative signs are because the radius and the volume 
are both decreasing.

Edwin